How can I solve the sludge problem in a Toyota Camry?

You can either replace the transmission or do a full systems fluid flush, this in general can fix most sludge related problems. This is a fairly difficult repair, if you consider yourself a novice I would recommend either consulting your car manual, or seeking the help of a licensed mechanic to-be safe.

On next oil change, substitute one quart of transmission oil for one quart engine oil. Then Add the rest in the camry. Drive around for a day and then do second oil change and only use all engine oil. If problem persist repeat steps all over again. If this doesn't resolve the issue, take to dealership to fix problem.

When you do the next oil change you substitute one quart of transmission oil for one quart engine oil. Add the rest of the oil that is required for your Camry. Drive around for a day or so. Do a second oil change and use all engine oil. If there is still a problem drain and repeat steps above!

If you have sludge build up from improper oil changes and engine maintenance the best thing to do is rebuild the engine. That will allow you to use solvent to remove all the deposits. Otherwise you can remove most of it by doing frequent oil changes every few thousand miles with a high quality oil.

Changing to a high quality oil that is designed to cut down on sludge and clean your engine should be all that you need to do get rid of this pesky problem. Make sure you completely drain all your oil and change it out completely.